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The stress tensor

The stress tensor. Section 2. “ Undeformed ” body means…. “Deformed” body means…. Internal stresses are…. k th component of area element d f , which is along outward normal of portion. Moment of forces on portion (torque). Vanishes if stress is symmetric, TBD.

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The stress tensor

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  1. The stress tensor Section 2

  2. “Undeformed” body means…

  3. “Deformed” body means…

  4. Internal stresses are…

  5. kth component of area element df, which is along outward normal of portion

  6. Moment of forces on portion (torque)

  7. Vanishes if stress is symmetric, TBD

  8. Then Mik is a surface integral, as required

  9. Hydrostatic compression: Pressure of same magnitude acts on every unit area of the surface of the body along the inward normal.

  10. Arbitrary deformation

  11. Equilibrium: Internal stresses balanceFi = 0 in every dV

  12. External forces applied to body surface appear in equations of equilibrum as boundary conditions

  13. Proof of sik symmetry

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